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Scheduling with Outliers
"... Abstract. In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs? Instead, we can schedule any subset of jobs whose total profi ..."
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Abstract. In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs? Instead, we can schedule any subset of jobs whose total profit is at least a (hard) target profit requirement, while still trying to approximately minimize the objective function. We refer to this class of problems as scheduling with outliers. This model was initiated by Charikar and Khuller (SODA ’06) for minimum maxresponse time in broadcast scheduling. In this paper, we consider three other wellstudied scheduling objectives: the generalized assignment problem, average weighted completion time, and average flow time, for which LPbased approximation algorithms are provided. Our main results are: – For the minimum average flow time problem on identical machines, we give an LPbased logarithmic approximation algorithm for the unit profits case, and complement this result by presenting a matching integrality gap. – For the average weighted completion time problem on unrelated machines, we give a constantfactor approximation. The algorithm is based on randomized rounding of the timeindexed LP relaxation strengthened by knapsackcover inequalities. – For the generalized assignment problem with outliers, we outline a simple reduction to GAP without outliers to obtain an algorithm whose makespan is within 3 times the optimum makespan, and whose cost is at most (1 + ɛ) times the optimal cost. 1
Improved Approximations for Guarding 1.5Dimensional Terrains
"... We present a 4approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (see [14]). Unlike most of the previous techniques, our method is base ..."
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We present a 4approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (see [14]). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.